Introduction: For some situations one can use an alternative formulation of the Monotonicity condition extremum.
Theorem: Assume $c$ is the only stationary point of a function $y(x)$ on an interval and $a$ is a point to the left of $c$ and $b$ a point to the right of $c$ such that $a<c<b$. It holds that:
Theorem: Assume $c$ is the only stationary point of a function $y(x)$ on an interval and $a$ is a point to the left of $c$ and $b$ a point to the right of $c$ such that $a<c<b$. It holds that:
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if $y(a)>y(c)$ and $y(b)>y(c)$, then $y(c)$ is a minimum;
- if $y(a)<y(c)$ and $y(b)<y(c)$, then $y(c)$ is a maximum.